Chaotic sequences are potentially attractive in a range of engineering applications such as broadband communication, radar application, and pattern recognition. Most such applications require, as a minimum, an accurate estimation of the actual chaotic sequence from a noisy signal. Classical signal-processing techniques are not adequate for this class of signals, which behave like noise although they are deterministic in nature. Consequently it is important to develop new algorithms for robust and efficient estimation of these signals in noise. Some such algorithms are currently available. Most are limited to ideal situations with very high signal-to-noise ratios. This paper presents a novel algorithm to estimate the initial condition of a chaotic signal (and hence the chaotic sequence if the mapping function is known). It is a general algorithm that can be of broad use. It is also shown to outperform standard algorithms that are in current use. This split-region approach is applicable for a wide range of signal-to-noise ratios, and provides reasonable estimates down to 5 dB.